Advertisements
Advertisements
Question
Find the differential equation of system of concentric circles with centre (1, 2).
Advertisements
Solution
Family of concentric circles with centre (1, 2) and radius ‘r’ is (x – 1)2 + (y – 2)2 = r2
Differentiating both sides w.r.t., x we get
`2(x - 1) + 2(y - 2) "dy"/"dx"` = 0
⇒ `(x - 1) + (y - 2) "dy"/"dx"` = 0
Which is the required equation.
APPEARS IN
RELATED QUESTIONS
Form the differential equation of the family of ellipses having foci on y-axis and centre at origin.
Form the differential equation of the family of hyperbolas having foci on x-axis and centre at origin.
Which of the following differential equations has y = c1 ex + c2 e–x as the general solution?
(A) `(d^2y)/(dx^2) + y = 0`
(B) `(d^2y)/(dx^2) - y = 0`
(C) `(d^2y)/(dx^2) + 1 = 0`
(D) `(d^2y)/(dx^2) - 1 = 0`
Form the differential equation from the following primitive where constants are arbitrary:
y = cx + 2c2 + c3
Form the differential equation from the following primitive where constants are arbitrary:
xy = a2
Form the differential equation corresponding to y2 = a (b − x2) by eliminating a and b.
Form the differential equation corresponding to (x − a)2 + (y − b)2 = r2 by eliminating a and b.
Form the differential equation of the family of curves represented by the equation (a being the parameter):
(2x − a)2 − y2 = a2
Form the differential equation of the family of curves represented by the equation (a being the parameter):
(x − a)2 + 2y2 = a2
Represent the following families of curves by forming the corresponding differential equations (a, b being parameters):
x2 + y2 = a2
Represent the following families of curves by forming the corresponding differential equations (a, b being parameters):
y2 = 4ax
Represent the following families of curves by forming the corresponding differential equations (a, b being parameters):
y2 = 4a (x − b)
Represent the following families of curves by forming the corresponding differential equations (a, b being parameters):
y = ax3
Represent the following families of curves by forming the corresponding differential equations (a, b being parameters):
y = eax
Form the differential equation of the family of circles in the second quadrant and touching the coordinate axes.
Show that y = bex + ce2x is a solution of the differential equation, \[\frac{d^2 y}{d x^2} - 3\frac{dy}{dx} + 2y = 0\]
Find one-parameter families of solution curves of the following differential equation:-
\[\frac{dy}{dx} + 3y = e^{mx}\], m is a given real number.
Find one-parameter families of solution curves of the following differential equation:-
\[x\frac{dy}{dx} + y = x^4\]
Find one-parameter families of solution curves of the following differential equation:-
\[\left( x \log x \right)\frac{dy}{dx} + y = \log x\]
Find one-parameter families of solution curves of the following differential equation:-
\[\frac{dy}{dx} - \frac{2xy}{1 + x^2} = x^2 + 2\]
Find one-parameter families of solution curves of the following differential equation:-
\[\frac{dy}{dx} + y \cos x = e^{\sin x} \cos x\]
Find one-parameter families of solution curves of the following differential equation:-
\[\left( x + y \right)\frac{dy}{dx} = 1\]
The family of curves in which the sub tangent at any point of a curve is double the abscissae, is given by
Form the differential equation of the family of ellipses having foci on y-axis and centre at the origin.
Form the differential equation representing the family of curves y = A sin x, by eliminating the arbitrary constant A.
Find the differential equation of the family of curves y = Ae2x + B.e–2x.
Find the equation of a curve passing through the point (1, 1) if the perpendicular distance of the origin from the normal at any point P(x, y) of the curve is equal to the distance of P from the x-axis.
The solution of the differential equation `2x * "dy"/"dx" y` = 3 represents a family of ______.
Form the differential equation by eliminating A and B in Ax2 + By2 = 1
Find the equation of a curve passing through (2, 1) if the slope of the tangent to the curve at any point (x, y) is `(x^2 + y^2)/(2xy)`.
Find the equation of a curve passing through origin if the slope of the tangent to the curve at any point (x, y) is equal to the square of the difference of the abcissa and ordinate of the point.
The differential equation of the family of curves y2 = 4a(x + a) is ______.
The differential equation representing the family of circles x2 + (y – a)2 = a2 will be of order two.
From the differential equation of the family of circles touching the y-axis at origin
